What happens to the acceleration of an object if the mass stays the same and the force is tripled?

Chapter 5 – Newton’s Laws: Forces and Motion

Recap and Summary

1. Are the following statements true or false? Explain your answer using an example.

a. Applying a force to an object will make it move.

False. If you push on a wall it does not move.

b. To keep an object moving, a force must be applied.

False. Inertia and Newton’s 2nd law – an object in motion stays in motion unless acted upon by an outside force – like friction or air resistance.

c. A force must be applied to change the direction of a moving object.

True. An object moves in straight-line motion but to change direction you need to apply a force.

2. How can rolling a bowling ball help you to determine the amount of matter in the ball?

Determine the force required to accelerate the ball and determine the acceleration of the ball then use m = F / a.

3. List at least three parts of an automobile that are designed to overcome the effects of Newton’s first law. Briefly explain the function of each.

Accelerator, brake, steering wheel

4. Explain the difference between mass and weight. State common units for both quantities. How do you convert between the two quantities?

Mass is a measure of the amount of matter in an object while weight is the pull of gravity on the matter in an object. Mass is measured in kilograms while weight is measured in newtons. Mass x 10 = weight.

5. What is the difference between the terms “force” and “net force”?

Force is the applied potential. Net force is the sum of all forces acting on an object.

6. What do the positive and negative signs indicate in physics problems involving velocities, acceleration, and forces?

Positive tells you to the right or up or there is an increase. Negative tells you to the left or down or there is a decrease.

7. Label the signs of the net force, velocity, and acceleration for the following ramps.

8. What do motionless objects have in common with objects that are moving in a straight line with constant speed?

Both objects moving at a constant speed and stationary objects are in static equilibrium meaning they have zero net force.

9. You and your six-year-old cousin are wearing ice skates. You push off each other and move in opposite directions. How does the force you feel during the push compare to the force your cousin feels? How do your accelerations compare? Explain.

We both feel the same force, since the action-reaction pair is a set of equal magnitude forces in opposite directions.

Since we both feel the same force but my cousin has a smaller mass, my cousin will feel a larger acceleration.

10. Explain the motion of swimming in terms of Newton’s third law.

You push backward on the water and the water pushes forward on you – propelling you through the water.

11. You jump up. The Earth does not move a measurable amount. Explain this scenario using all three of Newton’s laws of motion.

1st – the earth at rest wishes to remain at rest.

2nd – the force you apply is too small to accomplish a significant acceleration of the earth’s large mass.

3rd – you push on the earth and the earth pushes back on you.

12. How does the inertia of a 200kg object compare to the inertia of a 400kg object?

The inertia of a 200kg object is half the inertia of a 400kg object.

13. A constant force is applied to a cart, causing it to accelerate. If the mass of the cart is tripled, what change occurs in the acceleration of the cart?

If the mass if tripled, the acceleration becomes one-third of its original acceleration – since acceleration is inversely proportional to the mass.

14. If the net force acting on an object is tripled, what happens to its acceleration?

If the force is tripled, the acceleration also triples since acceleration is directly proportional to force.

15. A 60kg boy rolls downhill on a bicycle that has a mass of 12kg. What net force is acting on the boy and his bicycle if he accelerates at a rate of 3.25 m/s2?

F = m a F = (72kg)(3.25m/s2) = 234N

16. As a baseball player strikes the ball with his bat, the 1-kg bat applies an average force of 500N on the 0.15-kg baseball for 0.20 seconds.

a. What force is applied by the baseball on the bat? F = -500N

b. What is the acceleration of the baseball? A = F/m = 500N/0.15kg = 3333.33 m/s2

c. What is the speed of the baseball at the end of the 0.2 seconds?

v = vo + at = (3333.33m/s2)(0.2s) = 666.67m/s

Isaac Newton's First Law of Motion states, "A body at rest will remain at rest, and a body in motion will remain in motion unless it is acted upon by an external force." What, then, happens to a body when an external force is applied to it? That situation is described by Newton's Second Law of Motion.

According to NASA, this law states, "Force is equal to the change in momentum per change in time. For a constant mass, force equals mass times acceleration." This is written in mathematical form as F = ma

F is force, m is mass and a is acceleration. The math behind this is quite simple. If you double the force, you double the acceleration, but if you double the mass, you cut the acceleration in half.

Newton published his laws of motion in 1687, in his seminal work "Philosophiæ Naturalis Principia Mathematica" (Mathematical Principles of Natural Philosophy) in which he formalized the description of how massive bodies move under the influence of external forces.

Newton expanded upon the earlier work of Galileo Galilei, who developed the first accurate laws of motion for masses, according to Greg Bothun, a physics professor at the University of Oregon. Galileo's experiments showed that all bodies accelerate at the same rate regardless of size or mass. Newton also critiqued and expanded on the work of Rene Descartes, who also published a set of laws of nature in 1644, two years after Newton was born. Descartes' laws are very similar to Newton's first law of motion.

Newton's second law says that when a constant force acts on a massive body, it causes it to accelerate, i.e., to change its velocity, at a constant rate. In the simplest case, a force applied to an object at rest causes it to accelerate in the direction of the force. However, if the object is already in motion, or if this situation is viewed from a moving inertial reference frame, that body might appear to speed up, slow down, or change direction depending on the direction of the force and the directions that the object and reference frame are moving relative to each other.

The bold letters F and a in the equation indicate that force and acceleration are vector quantities, which means they have both magnitude and direction. The force can be a single force or it can be the combination of more than one force. In this case, we would write the equation as ∑F = ma

The large Σ (the Greek letter sigma) represents the vector sum of all the forces, or the net force, acting on a body.

It is rather difficult to imagine applying a constant force to a body for an indefinite length of time. In most cases, forces can only be applied for a limited time, producing what is called impulse. For a massive body moving in an inertial reference frame without any other forces such as friction acting on it, a certain impulse will cause a certain change in its velocity. The body might speed up, slow down or change direction, after which, the body will continue moving at a new constant velocity (unless, of course, the impulse causes the body to stop).

There is one situation, however, in which we do encounter a constant force — the force due to gravitational acceleration, which causes massive bodies to exert a downward force on the Earth. In this case, the constant acceleration due to gravity is written as g, and Newton's Second Law becomes F = mg. Notice that in this case, F and g are not conventionally written as vectors, because they are always pointing in the same direction, down.

The product of mass times gravitational acceleration, mg, is known as weight, which is just another kind of force. Without gravity, a massive body has no weight, and without a massive body, gravity cannot produce a force. In order to overcome gravity and lift a massive body, you must produce an upward force ma that is greater than the downward gravitational force mg.

Newton's second law in action

Rockets traveling through space encompass all three of Newton's laws of motion.

If the rocket needs to slow down, speed up, or change direction, a force is used to give it a push, typically coming from the engine. The amount of the force and the location where it is providing the push can change either or both the speed (the magnitude part of acceleration) and direction.

Now that we know how a massive body in an inertial reference frame behaves when it subjected to an outside force, such as how the engines creating the push maneuver the rocket, what happens to the body that is exerting that force? That situation is described by Newton’s Third Law of Motion.

Additional reporting by Rachel Ross, Live Science contributor.

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